Solve for x x-9+2wx=y for x

$x - 9 + 2 w x = y$ for $x$

Add $9$ to both sides of the equation.

$x + 2 w x = y + 9$

Factor $x$ out of $x + 2 w x$ .

Factor $x$ out of $x^{1}$ .

$x \cdot 1 + 2 w x = y + 9$

Factor $x$ out of $2 w x$ .

$x \cdot 1 + x (2 w) = y + 9$

Factor $x$ out of $x \cdot 1 + x (2 w)$ .

$x (1 + 2 w) = y + 9$

Divide each term in $x (1 + 2 w) = y + 9$ by $1 + 2 w$ and simplify.

Divide each term in $x (1 + 2 w) = y + 9$ by $1 + 2 w$ .

$\frac{x (1 + 2 w)}{1 + 2 w} = \frac{y}{1 + 2 w} + \frac{9}{1 + 2 w}$

Simplify the left side.

Cancel the common factor of $1 + 2 w$ .

Cancel the common factor.

$\frac{x (1 + 2 w)}{1 + 2 w} = \frac{y}{1 + 2 w} + \frac{9}{1 + 2 w}$

Divide $x$ by $1$ .

$x = \frac{y}{1 + 2 w} + \frac{9}{1 + 2 w}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{y + 9}{1 + 2 w}$